Networks can be analysed by counting and classifying subgraphs within a graph [1]}, [2]}, [3]}, [4]}, [5]}, [6]}, [7]}, [8]}. The subgraph counting problem [4]}, [8]} consists of counting the number of subgraphs that are isomorphic to a given pattern graph \(H\)  in a graph \(G\) . Counting subgraphs is a hard problem, since it generalises the subgraph isomorphism problem, which is NP-complete [11]}.
Given the hardness of this problem, as many networks are increasingly large, there is a need for efficient algorithms to count subgraphs in a timely manner, or even to obtain good bounds on counts of these subgraphs. A comprehensive comparison between exact and approximate subgraph counting algorithms is given in [8]}.
